One for the math guys HELP please????

[Kairomancer]

I think this formula is way too risky. It does not account for variance.

Let's suppose you play european roulette with a huge advantage and bet exclusively single numbers with an expected hit rate of 1 in18. The payout is obviously 35 units.
According to the formula you have to bet around 2,8% percent of your bankroll.
In case you hit a bad run and miss your number 35 times you quickly lose most of your initial bankroll.

Negative progressions with a stop loss are much safer choice.

[bikemotorman]

Ok, guys I just found this nice Kelly Calculator.

link:s://:.albionresearch.com/kelly/default.php

[bikemotorman]

A Kelly Strategy Calculator

link:s://:.albionresearch.com/kelly/default.php



A Kelly Strategy Calculator
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Introduction
J.L.Kelly, in his seminal paper A New Interpretation of Information Rate (Bell System Technical Journal, 35, 917-926 see below) asked the interesting question: how much of my bankroll should I stake on a bet if the odds are in my favour? This is the same question that a business owner, investor, or speculator has to ask themselves: what proportion of my capital should I stake on a risky venture?

Kelly did not, of course, use those precise words â€" the paper being written in terms of an imaginary scenario involving bookies, noisy telephone lines, and wiretaps so that it could be published by the prestigious Bell System Technical Journal.

Assuming that your criterion is the same as Kelly's criterion â€" maximizing the long-term growth rate of your fortune â€" the answer Kelly gives is to stake the fraction of your gambling or investment bankroll which exactly equals your advantage. The form below allows you to determine what that amount is.

Please read the disclaimer, if you haven't done so already.

Gambling Bankroll:   $
250
Odds offered:   
1
to 
1
e.g. 7 to 4, 2 to 1, etc.
Odds of 2 to 1 on should be entered as 1 to 2,
Odds of 11 to 10 on should be entered as 10 to 11
Your estimate of your
The probability of Winning:   
51
% Use a conservative (low) estimate.
Bets must be multiples of $
1.00
The minimum bet allowed is:   $
5.00

Results
The odds are in your favour, but read the following carefully:
According to the Kelly criterion, your optimal bet is about 2% of your capital, or $5.00.
On 51% of similar occasions, you would expect to gain $5.00 in addition to your stake of $5.00 being returned.
But on those occasions when you lose, you will lose your stake of $5.00.
Your fortune will grow, on average, by about 0.02% on each bet.
Bets have been rounded down to the nearest multiple of $1.00.
If you do not bet exactly $5.00, you should bet less than $5.00.
The outcome of this bet is assumed to have no relationship to any other bet you make.
The Kelly criterion is maximally aggressive â€" it seeks to increase capital at the maximum rate possible. Professional gamblers typically take a less aggressive approach, and generally won't bet more than about 2.5% of their bankroll on any wager. In this case that would be $5.00.
A common strategy (see discussion below) is to wager half the Kelly amount, which in this case would be $2.00.
If your estimated probability of 51% is too high, you will bet too much and lose over time. Make sure you are using a conservative (low) estimate.
Please read the disclaimer as well as the notes below.
More Information
The BJ Math site used to contain a great collection of papers on Kelly betting, including the original Kelly Bell Technical System Journal paper. Unfortunately, it is now defunct, and only contains adverts for an online casino. However, you can find much of the content through the Wayback Machine archive. The Internet Archive also contains a copy of Kelly's original paper which appeared as A New Interpretation of Information Rate, Bell System Technical Journal, Vol. 35, pp917-926, July 1956. (If this link breaks â€" as it has done several time since this page was written â€" try searching for the article title).

We based the above calculations on the description given in the book Taking Chances: Winning With Probability by John Haigh, which is an excellent introduction to the mathematics of probability. (Note that there is a misprint in the formula for approximating average growth rate on p359 (2nd edition) and the approximation also assumes that your advantage is small. There is a short list of corrections which can be found through John Haigh's web page).

Note that although the Kelly Criterion provides an upper bound on the amount that should be risked, there are sound arguments for risking less. In particular, the Kelly fraction assumes an infinitely long sequence of wagers â€" but in the long run we are all dead. It can be shown that a Kelly bettor has a 1/3 chance of having a bankroll before doubling it, and that you have a 1/n chance or reducing your bankroll to 1/n at some point in the future. For comparison, a “half kelly” bettor only has a 1/9 chance of halving their bankroll before doubling it. There's an interesting discussion of this (not aimed at a mathematical reader) in Part 4 of the book Fortune's Formula which gives some of the history of the Kelly criterion, along with some of its notable successes and failures.

Jeffrey Ma was one of the members of the MIT Blackjack Team, a team which developed a system based on the Kelly criterion, card counting, and team play to beat casinos at Blackjack. He has written an interesting book The House Advantage, which examines what he learned about managing risk from playing blackjack. (He also covers some of the measures put in place by casinos to prevent the team winning!)

[bikemotorman]

So the Kelly method is kind of like flat betting but not really, I am going to ask my playing partner to see if we can try it out.

We flat bet most of the time, however, we do at times do a two bet then once in a while a three-bet just to get back to even.
Our max loss is eight units.

Here is the link address if you use it for Baccarat it is 50/50 or 1 to 1.

link:s://:.albionresearch.com/kelly/default.php


Stuart

[Joe]

I think this formula is way too risky. It does not account for variance.

Yes that's a recognized weakness of the Kelly. Often punters prefer to use "half" Kelly or even "quarter" Kelly.

[The General]

Yes that's a recognized weakness of the Kelly. Often punters prefer to use "half" Kelly or even "quarter" Kelly.

In roulette we incorporated an additonal variable that represents confidence level in the playing conditions.  For example if the confidence level is at 60% then you multiply that times your betting percentage to move it down in value.

Edge/expectancy x confidence level = bank to bet ratio

Unless you have the edge in bac or roulette the Kelly isn't going to help.  As a matter of fact the results it gives you will be a negative value.  Rather than focusing so much on the progression you should first worry about how to get the edge.

[luckyfella]

The purpose of kelly formula is to maximise the utility of the outcomes

The key word here is maximise

The problem with kelly formula is in the application side

The user in his decision making process has maximum utility and capital preservation among the criteria how his portfolio grows

By maximum utility, Kelly formula do see large volatility that the user may not be comfortable with

It uses the math calculated expected value
However, most users tend to have a lower expected value that is risk averse that reflect more of their capital preservation focus
Hence, this math formula is peppered downwards to the degree to bring it inline with the users risk tolerance

[The General]

The Kelly only works if you already have the edge.

If you don't have the edge, then you can't play the Kelly progression.

[nottophammer]

link:s://:.youtube.com/watch?v=qTkkSMAL2h8
Over the edge

[Kairomancer]

In roulette we incorporated an additonal variable that represents confidence level in the playing conditions.  For example if the confidence level is at 60% then you multiply that times your betting percentage to move it down in value.

Edge/expectancy x confidence level = bank to bet ratio

The problem is that your confidence level is highly subjective value to incorporate it into mathematically sound formula.

In other words you are just making guesses.
Progressions with stop loss in most cases are still better choice.

Though your modified formula could be used as a starting base bet then add progressions to maximize profit

Why guessing when you can be sure that you eventually almost always hit your profit mark in most sessions.

[bikemotorman]

Yes we do have an edge we win about 52 percent of the hands we play in Baccarat on Betphoenix and the results have been quite good, we did have a few days where it got a bit rough but I was advised hang on Stuart we are only down 16 units.
I got anxious instead of trusting our bet selection but since then its been much better we have refined the process to be more efficient.
We started at 5 dollar units and built our bank up so we could go up to 10 dollar units.
In reality, we are winning more like 54 or 55 percent but I low balled it just in case we have some more rough shoes.

I am working on the making sure to stick to the method and not move the goalposts so to speak like we have heard so many people do at times PATIENCE AND DICIPLINE.

At the time I find myself getting upset if I lose a few plays but steady and bits of patience is a skill I am getting better at, my playing partner will say ok we have won six units let us quit till later in the day and I want to grind out some more wins but he is very steadfast on how the rules work.

I am learning guys remember as LANKY used to say PATIENCE AND DICIPLINE.

Stuart

[bikemotorman]

I forgot to mention our MAX LOSS is 8 units for the day.

Stuart

[Joe]

If you don't have the edge, then you can't play the Kelly progression.

Correction, you can play it, but you will lose, through not as much as you would if using a negative progression. However I agree with you that the first order of business should be getting the edge; no progression, no matter how large your bank, will give you that.

[Roulettebeater]

Stu, it's really easy, honest!

Forget about the formula, all you do is to take your starting bank and the first bet is 2% of it. So if it's $100 your first bet is 0.02 * 100 = $2

Suppose you win this bet, your bank is now $102. Just do the same again, 2% of $102 is 0.02 * 102 = 2.04. Since you can't bet $2.04 you just round it up or down. If the result is more than $2.5 you round it up to $3, and if it's less you round down to $2, so the next bet is also $2.
Suppose you win the next bet, your bank is now $104. To calculate the next stake you just do the same again (it never changes!), so your stake is 0.02 * 104 = $2.08, so round down to $2. Since you have an edge your bank will soon get to the point where your stake increase to $3, then $4, etc, but if you hit a losing run the stake will go down because the stakes are always proportional to the size of your bank. See how it works?
It's much much easier than the 6 point divisor plan. Whatever your bank is you just multiply by 0.02 to get the next stake, that's it. ;-)

You only have to use the formula if your edge and/or the odds of the bet changes.

JoeCoder,

What are the pro of this staking plan? can you please tell me why you recommending it?

thx

[Joe]

RB, I posted a link in a previous post which explains it. I'm recommending it because nothing beats it in terms of compounding your winnings (assuming you have an edge), although it does have its downsides.
From Wikipedia :

In probability theory and intertemporal portfolio choice, the Kelly criterion, Kelly strategy, Kelly formula, or Kelly bet is a formula used to determine the optimal size of a series of bets in order to maximise the logarithm of wealth. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any essentially different strategy in the long run (that is, over a span of time in which the observed fraction of bets that are successful equals the probability that any given bet will be successful).